To assess the fit of a fitted model, it is necessary to compare the realizations
and the replicates using many different statistics, all of which summarize
different aspects of the disordered patterns within each realization or
trajectory. Some of these statistics will be chosen to seek out possible
differences between model and experimental trajectories based on
what is known about the physics of powders, but others must be chosen
from a large library of descriptive statistics which compare other aspects
of the trajectories. These additional statistics are required to seek out
differences which neither the eye can see nor existing theory
would suggest looking for. It will be necessary to develop extensive
libraries of statistics for this purpose, which will include \(k-\) point correlation functions, point process statistics [1]},
tessellation-based statistics [2]}, [3]}, statistics based on mathematical models
for physical processes applied in a non-physical context [4]},
statistics found useful in the analyses of other experiments, and many other
descriptors of ordered structure which have not yet been invented.
